# Re: The Big Bang

04 Nov 1997 22:48:39 +0100

Greg Butler <gsb1997@ix.netcom.com> writes:

> On Tuesday, November 04, 1997 8:54 AM, Anders Sandberg
> > No. The amount of radiation you get from a star decreases with the
> > square of the distance. But the number of stars grows with the square
> > of the distance, so the total radiation from a given distance is
> > approximately constant.
>
> I don't understand how one can compare one infinite number
> with another (such as an infinite volume of space and an infinite
> number of stars). If there is an infinite space per star, it seems
> possible that it won't get filled. One infinite amount does not
> necessarily equal another. For instance, how big is an infinite
> amount of space squared? Is it bigger than a "regular" infinite
> amount? Greg

Ok, wait a moment while I don my impressive mathematicians robe
(complete with chalk dust)... :-)

Infinities are tricky, but if you know the rules and are a bit careful
you can handle them with no danger. Yes, there are differently "sized"
infinities, some much "larger" than others. But in this case it is
much simpler.

In the star example, let's say there are around 1 star per cubic
lightyear. That means that on a sphere of radius r there will be
around 4 Pi r^2 stars. The intensity of a star at distance r is L/r^2
where L is a constant (I assume all stars are equally bright now, for
simplicitys sake). This means that the 4 pi r^2 stars on the sphere
around us will shine with a total power of 4 Pi L - the two r^2 terms
cancel each other. So the total luminosity from a spherical shell
around us is independent of it's radius. This means that if we get one
unit of light from all stars 1 lightyear away, we will get one unit
from the stars 2 lightyears away, one from all stars 3 lightyears
away, and so on. As you sum up the contributions from all the shells
the sum get's larger and larger. And if you assume an infinite
universe you will have to sum up the contributions of ever more remote
stars, and the total luminosity will become larger than any finite
luminosity.

If you want a real in depth treatment of infinities, I suggest reading
up on basic calculus and perhaps set theory.

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Anders Sandberg                                      Towards Ascension!